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Coordination sequence Gal.5.19.1 where Gal.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
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%I #14 Oct 21 2023 15:10:32

%S 1,3,6,11,15,19,23,25,28,31,34,41,45,49,53,53,56,59,62,71,75,79,83,81,

%T 84,87,90,101,105,109,113,109,112,115,118,131,135,139,143,137,140,143,

%U 146,161,165,169,173,165,168,171

%N Coordination sequence Gal.5.19.1 where Gal.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.

%C Note that there may be other vertices in the Galebach list of u-uniform tilings with u <= 6 that have this same coordination sequence. See the Galebach link for the complete list of A-numbers for all these tilings.

%C Conjectures from _Colin Barker_, Apr 18 2020: (Start)

%C G.f.: (1 + 2*x + 3*x^2 + 5*x^3 + 5*x^4 + 6*x^5 + 7*x^6 + 7*x^7 + 6*x^8 + 5*x^9 + 4*x^10 + 4*x^11 + 2*x^12 + x^13) / ((1 - x)^2*(1 + x)*(1 + x^2)*(1 + x^4)^2).

%C a(n) = a(n-1) - a(n-4) + a(n-5) + a(n-8) - a(n-9) + a(n-12) - a(n-13) for n>13.

%C (End)

%H Brian Galebach, <a href="/A250120/a250120.html">k-uniform tilings (k <= 6) and their A-numbers</a>

%K nonn

%O 0,2

%A _Brian Galebach_ and _N. J. A. Sloane_, Jun 18 2018

%E Edited by _Georg Fischer_, Apr 17 2020